new graphical method to estimate the optimal repair-time limit with incomplete repair and discounting

In this paper, we consider a repair-time limit replacement problem with imperfect repair and discounting, and focus on the problem to determine the optimal repair-time limit which minimizes the expected total discounted cost over an infinite time horizon. Based upon a sophisticated graphical idea, we develop a nonparametric method to estimate the optimal repair-time limit from the empirical repair-time data. Numerical examples are devoted to estimate the optimal policy and to examine the asymptotic properties of the estimator.